Page 52 - Contributed Paper Session (CPS) - Volume 1

CPS863 Abubakar S. A. et al.
each quarter using the design chosen from Phase 2 of the simulation (e.g.,
PPS-SYS). (2) Draw sample households from each barangay of size =
( , ,··· , ). (3) Compute for = ( , , … , )from the original sample
̂
̂ ̂
̂
2
2
1

1

̂

where = ( ) , = ∑ and is the probability of selection of

=1
barangay computed as the reciprocal of the design weight for barangay .
Each will serve as an estimate of PSU total and will serve as the pseudo-
̂
̂

population. (4) Generate size bootstrap sample from using SRSWOR.
̂

nd
2.3.2 Modified Bootstrap 2 Stage
Resampling is done at the second stage (selection of sample corn farm
households). Steps: (1) Same steps as in 1 and 2 of Modified Bootstrap 1
st
∗
∗
∗
∗
Stage. (2) Let = ( ) , ( ) , … , ( ) where ∗ is the vector of
1

2

2
rounded-up elements of = 1 2 , … , where , , … , ℎ is the
,

2
1
1 2
number of sample corn farm households in barangays 1,2,…,α while
, , … , is the total number of corn farm households in barangays 1,2,…,α.
2
1

(3) Generate by copying each households from each sampled barangays
∗
times and generate new households IDs for these. (4) Draw = 500
∗

samples of size households using SRSWOR from each barangay from .
∗
̂
=1
The bootstrap estimator of total corn production is = ∑ ̂ , =

̂
1,2,3, … , , = ∑ ∑ , ≡ weight of barangay computed via

=1
=1
PPS-SYS and = corn production for household , barangay . The estimator

̂

of variance is ( ) = ∑ ( ̂ − ) 2 .
=1

−1

2.4 Phase 4: Model for Estimation of Corn Production
Corn production in the country is highly a↵ected by seasonal patterns
brought about by variations in climate and soil types8. Provinces that
contribute to the 97% of the total corn production were considered top
producing were surveyed. However, nontop producing provinces of a quarter
were un-surveyed, and their corn production was estimated using models.
Three models were developed for the estimation.

2.4.1 Model 1
A mixed effect model with standing crop area as fixed e↵ects and municipal
2
as random effect. = + −1 + + , ∽ (0, ), ≡ total

production at municipality on quarter , −1 ≡ total standing crop of
municipality at quarter − 1 and ~(0, ), where G≡ variance-covariance

matrix of the random effect.

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